Efficiency estimation for an equilibrium version of Maxwell refrigerator

TL;DR

This paper analyzes a simplified Maxwell refrigerator model, deriving efficiency and COP, showing maximum efficiency aligns with Carnot limits, and exploring how power and performance depend on temperature and energy level parameters.

Contribution

It introduces a simplified equilibrium version of the Maxwell refrigerator and derives explicit formulas for efficiency and COP, extending understanding of thermodynamic limits in information-based devices.

Findings

Maximum efficiency matches Carnot efficiency.

COP at maximum power decreases with increasing hot reservoir temperature.

Efficiency at maximum power follows a specific formula depending on temperature and energy level.

Abstract

Maxwell refrigerator as a device that can transfer heat from a cold to hot temperature reservoir making use of information reservoir was introduced by Mandal et al. \cite{Mandal2013a}. The model has a two state demon and a bit stream interacting with two thermal reservoirs simultaneously. We work out a simpler version of the refrigerator where the demon and bit system interact with the reservoirs separately and for a duration long enough to establish equilibrium. The efficiency, $\eta$, of the device when working as an engine as well as the coefficient of performance (COP) when working as a refrigerator are calculated. It is shown that the maximum efficiency matches that of a Carnot engine/refrigerator working between the same temperatures, as expected. The COP at maximum power decreases as $\frac{1}{T_h}$ when $T_h >T_c \gg \Delta E$ ($k_B = 1$), where $T_h$ and $T_c$ are the temperatures of the hot and cold reservoirs respectively and $\Delta E$ is the level spacing of the demon. $\eta$ at maximum power of the device, when working as a heat engine, is found to be $\frac{T_h}{0.779 + T_h}$ when $T_c \ll \Delta E$ and $T_h \gg \Delta E$.